Beyond Canonical DC-Optimization: The Single Reverse Polar Problem

Giancarlo Bigi (), Antonio Frangioni () and Qinghua Zhang ()
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Giancarlo Bigi: Università di Pisa
Antonio Frangioni: Università di Pisa
Qinghua Zhang: Wuhan University

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 2, No 5, 430-452

Abstract: Abstract We propose a novel generalization of the Canonical Difference of Convex problem (CDC), and we study the convergence of outer approximation algorithms for its solution, which use an approximated oracle for checking the global optimality conditions. Although the approximated optimality conditions are similar to those of CDC, this new class of problems is shown to significantly differ from its special case. Indeed, outer approximation approaches for CDC need be substantially modified in order to cope with the more general problem, bringing to new algorithms. We develop a hierarchy of conditions that guarantee global convergence, and we build three different cutting plane algorithms relying on them.

Keywords: Single reverse polar problems; Approximate optimality conditions; Cutting plane algorithms (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-0069-7

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